Stats center

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Center

Which centre Levene's test measures each group's spread around.

public enum Center { Median, Mean, Trimmed }

Members — Median is the group's median, scipy's 'median', and the variant Brown and Forsythe published; it is the default on both sides. Mean is the group's mean, scipy's 'mean', and Levene's original test. Trimmed is the mean of what is left after dropping each end, scipy's 'trimmed'.

Example — the same three groups under two centres, which answer differently.

using Lodestar.Stats;

double[] first = [20.1, 19.8, 20.3, 20.0, 19.9, 20.2, 20.1, 19.7];
double[] second = [20.4, 18.9, 21.2, 19.1, 21.0, 18.7, 20.8, 19.4];
double[] third = [20.0, 20.1, 19.9, 20.2, 19.8, 20.1, 20.0, 19.9];

double median = Math.Round(Levene.Test(first, second, third).Statistic, 4);
double trimmed = Math.Round(
    Levene.Test(Center.Trimmed, 0.25, NanPolicy.Propagate, first, second, third).Statistic, 4);

double brownForsythe = median;   // => 45.3383
double quarterTrimmed = trimmed; // => 46.5678

Remarks — the choice is about what an outlier should be allowed to do. Centring on the mean lets one stray value pull the centre toward itself and inflate every deviation in that group, which reads as extra spread. The median does not move, so the group's own outlier shows up as one large deviation instead of many moderate ones. Trimming sits between the two, dropping int(n × proportionToCut) values from each end of the sorted group before averaging — truncated, which is scipy.stats.trim_mean's rule, so a small group and a small proportion can trim nothing at all and leave Trimmed identical to Mean.

Applies to — net10.0, netstandard2.0.

See also — Levene.Test, Bartlett.Test, the Python equivalence table.